Everyone’s perception is different, I’ve met someone who couldn’t tell the UFOs apart past 30 fps. They also didn’t like shooters/action games much, probably because following fast movements was difficult for them.
But I think the vast majority of people easily notice the difference between 30 and 60. And 60 to 120 should also be possible notice for most. As for me, I used to play Quake 3 a lot and back then that was played on 120 or even 240hz CRTs. The first flat screens with slow reaction times and 60hz max were quite a step down.
While I don’t really like linus tech tips, they did some nice testing on the topic and came to the conclusion that more fps is measurably better for shooters, even if the refresh rate can’t keep up.